Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1765.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.48079\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.7900 | 1.33853 | 0.669267 | − | 0.743022i | \(-0.266608\pi\) | ||||
0.669267 | + | 0.743022i | \(0.266608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.16892 | −0.223911 | −0.111956 | − | 0.993713i | \(-0.535711\pi\) | ||||
−0.111956 | + | 0.993713i | \(0.535711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.7694 | −0.997808 | −0.498904 | − | 0.866657i | \(-0.666264\pi\) | ||||
−0.498904 | + | 0.866657i | \(0.666264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 60.3173 | 0.860535 | 0.430267 | − | 0.902701i | \(-0.358419\pi\) | ||||
0.430267 | + | 0.902701i | \(0.358419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −111.802 | −1.34995 | −0.674975 | − | 0.737841i | \(-0.735845\pi\) | ||||
−0.674975 | + | 0.737841i | \(0.735845\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 36.9268 | 0.334772 | 0.167386 | − | 0.985891i | \(-0.446467\pi\) | ||||
0.167386 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.2627 | 0.212991 | 0.106495 | − | 0.994313i | \(-0.466037\pi\) | ||||
0.106495 | + | 0.994313i | \(0.466037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −124.274 | −0.720010 | −0.360005 | − | 0.932950i | \(-0.617225\pi\) | ||||
−0.360005 | + | 0.932950i | \(0.617225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −123.950 | −0.598610 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −438.610 | −1.94884 | −0.974419 | − | 0.224741i | \(-0.927846\pi\) | ||||
−0.974419 | + | 0.224741i | \(0.927846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 508.071 | 1.93530 | 0.967651 | − | 0.252291i | \(-0.0811840\pi\) | ||||
0.967651 | + | 0.252291i | \(0.0811840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.5247 | −0.172092 | −0.0860459 | − | 0.996291i | \(-0.527423\pi\) | ||||
−0.0860459 | + | 0.996291i | \(0.527423\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −248.030 | −0.769763 | −0.384881 | − | 0.922966i | \(-0.625758\pi\) | ||||
−0.384881 | + | 0.922966i | \(0.625758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 271.543 | 0.791672 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −320.404 | −0.830394 | −0.415197 | − | 0.909732i | \(-0.636287\pi\) | ||||
−0.415197 | + | 0.909732i | \(0.636287\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.8446 | 0.100136 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −652.268 | −1.43929 | −0.719645 | − | 0.694343i | \(-0.755695\pi\) | ||||
−0.719645 | + | 0.694343i | \(0.755695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 693.019 | 1.45462 | 0.727311 | − | 0.686308i | \(-0.240770\pi\) | ||||
0.727311 | + | 0.686308i | \(0.240770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 233.847 | 0.446233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0308 | −0.0219373 | −0.0109686 | − | 0.999940i | \(-0.503491\pi\) | ||||
−0.0109686 | + | 0.999940i | \(0.503491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1168.30 | 1.95284 | 0.976421 | − | 0.215877i | \(-0.0692609\pi\) | ||||
0.976421 | + | 0.215877i | \(0.0692609\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −122.195 | −0.195915 | −0.0979575 | − | 0.995191i | \(-0.531231\pi\) | ||||
−0.0979575 | + | 0.995191i | \(0.531231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −202.507 | −0.299712 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −441.669 | −0.629008 | −0.314504 | − | 0.949256i | \(-0.601838\pi\) | ||||
−0.314504 | + | 0.949256i | \(0.601838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 428.581 | 0.566782 | 0.283391 | − | 0.959004i | \(-0.408541\pi\) | ||||
0.283391 | + | 0.959004i | \(0.408541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −301.586 | −0.384843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1549.24 | −1.84515 | −0.922577 | − | 0.385813i | \(-0.873921\pi\) | ||||
−0.922577 | + | 0.385813i | \(0.873921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1159.41 | −1.33560 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 559.008 | 0.603716 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −500.136 | −0.523516 | −0.261758 | − | 0.965134i | \(-0.584302\pi\) | ||||
−0.261758 | + | 0.965134i | \(0.584302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −535.936 | −0.527997 | −0.263998 | − | 0.964523i | \(-0.585041\pi\) | ||||
−0.263998 | + | 0.964523i | \(0.585041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134.905 | −0.129055 | −0.0645273 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645273 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −808.631 | −0.730592 | −0.365296 | − | 0.930891i | \(-0.619032\pi\) | ||||
−0.365296 | + | 0.930891i | \(0.619032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1073.96 | −0.943730 | −0.471865 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471865 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 523.376 | 0.435709 | 0.217854 | − | 0.975981i | \(-0.430094\pi\) | ||||
0.217854 | + | 0.975981i | \(0.430094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −184.634 | −0.149715 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1495.26 | 1.15185 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1264.27 | −0.949864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −114.730 | −0.0801622 | −0.0400811 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400811 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −499.073 | −0.332857 | −0.166428 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166428 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2771.56 | −1.80695 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1887.38 | −1.17701 | −0.588504 | − | 0.808495i | \(-0.700283\pi\) | ||||
−0.588504 | + | 0.808495i | \(0.700283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1784.90 | −1.08916 | −0.544580 | − | 0.838709i | \(-0.683311\pi\) | ||||
−0.544580 | + | 0.838709i | \(0.683311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 382.056 | 0.223420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −166.313 | −0.0952522 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −996.321 | −0.547797 | −0.273899 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273899 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3487.14 | −1.87933 | −0.939666 | − | 0.342093i | \(-0.888864\pi\) | ||||
−0.939666 | + | 0.342093i | \(0.888864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 621.371 | 0.321998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1785.99 | −0.907880 | −0.453940 | − | 0.891032i | \(-0.649982\pi\) | ||||
−0.453940 | + | 0.891032i | \(0.649982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 915.415 | 0.448104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −396.237 | −0.190403 | −0.0952014 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952014 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1749.48 | 0.810654 | 0.405327 | − | 0.914172i | \(-0.367158\pi\) | ||||
0.405327 | + | 0.914172i | \(0.367158\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.61953 | −0.00437849 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2998.95 | −1.31796 | −0.658978 | − | 0.752162i | \(-0.729011\pi\) | ||||
−0.658978 | + | 0.752162i | \(0.729011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 619.750 | 0.267707 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 682.749 | 0.285090 | 0.142545 | − | 0.989788i | \(-0.454471\pi\) | ||||
0.142545 | + | 0.989788i | \(0.454471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 59.3943 | 0.0243909 | 0.0121954 | − | 0.999926i | \(-0.496118\pi\) | ||||
0.0121954 | + | 0.999926i | \(0.496118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2193.05 | 0.871546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −492.727 | −0.192683 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3618.13 | 1.37067 | 0.685336 | − | 0.728227i | \(-0.259655\pi\) | ||||
0.685336 | + | 0.728227i | \(0.259655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1536.37 | 0.573007 | 0.286504 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286504 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 136.471 | 0.0493561 | 0.0246780 | − | 0.999695i | \(-0.492144\pi\) | ||||
0.0246780 | + | 0.999695i | \(0.492144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −123.255 | −0.0439061 | −0.0219531 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219531 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 824.581 | 0.285095 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2540.36 | −0.865494 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 913.298 | 0.302269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4128.55 | 1.34702 | 0.673509 | − | 0.739179i | \(-0.264786\pi\) | ||||
0.673509 | + | 0.739179i | \(0.264786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 242.624 | 0.0769618 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3080.76 | −0.963758 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2821.01 | −0.858649 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3094.00 | −0.929102 | −0.464551 | − | 0.885546i | \(-0.653784\pi\) | ||||
−0.464551 | + | 0.885546i | \(0.653784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1399.26 | 0.409128 | 0.204564 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204564 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4787.68 | 1.38157 | 0.690784 | − | 0.723061i | \(-0.257265\pi\) | ||||
0.690784 | + | 0.723061i | \(0.257265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5117.74 | −1.43894 | −0.719472 | − | 0.694521i | \(-0.755616\pi\) | ||||
−0.719472 | + | 0.694521i | \(0.755616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1240.15 | 0.344248 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2813.92 | −0.761580 | −0.380790 | − | 0.924662i | \(-0.624348\pi\) | ||||
−0.380790 | + | 0.924662i | \(0.624348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3543.20 | −0.947045 | −0.473522 | − | 0.880782i | \(-0.657018\pi\) | ||||
−0.473522 | + | 0.880782i | \(0.657018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1357.72 | −0.354046 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5228.90 | 1.34699 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3446.10 | 0.866597 | 0.433299 | − | 0.901250i | \(-0.357350\pi\) | ||||
0.433299 | + | 0.901250i | \(0.357350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −301.652 | −0.0749593 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1354.83 | 0.328841 | 0.164421 | − | 0.986390i | \(-0.447425\pi\) | ||||
0.164421 | + | 0.986390i | \(0.447425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10873.1 | −2.60858 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −344.218 | −0.0807050 | −0.0403525 | − | 0.999186i | \(-0.512848\pi\) | ||||
−0.0403525 | + | 0.999186i | \(0.512848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1602.02 | 0.371363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 203.341 | 0.0460889 | 0.0230445 | − | 0.999734i | \(-0.492664\pi\) | ||||
0.0230445 | + | 0.999734i | \(0.492664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1586.34 | −0.355584 | −0.177792 | − | 0.984068i | \(-0.556895\pi\) | ||||
−0.177792 | + | 0.984068i | \(0.556895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −204.223 | −0.0447822 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4330.18 | −0.939260 | −0.469630 | − | 0.882863i | \(-0.655613\pi\) | ||||
−0.469630 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6569.00 | −1.39457 | −0.697284 | − | 0.716795i | \(-0.745609\pi\) | ||||
−0.697284 | + | 0.716795i | \(0.745609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −997.534 | −0.209531 | −0.104765 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104765 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12595.1 | 2.59047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1274.82 | −0.259480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 182.221 | 0.0363326 | 0.0181663 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181663 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3261.34 | 0.643670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1727.05 | −0.334039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1202.93 | −0.230351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3465.09 | −0.650527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1671.12 | 0.310670 | 0.155335 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155335 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9271.81 | −1.69053 | −0.845267 | − | 0.534345i | \(-0.820558\pi\) | ||||
−0.845267 | + | 0.534345i | \(0.820558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −572.410 | −0.103369 | −0.0516845 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516845 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6048.37 | 1.07164 | 0.535820 | − | 0.844332i | \(-0.320002\pi\) | ||||
0.535820 | + | 0.844332i | \(0.320002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −271.720 | −0.0476909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6743.57 | −1.16168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1169.24 | −0.199562 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6148.65 | −1.03035 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8537.53 | 1.41772 | 0.708860 | − | 0.705350i | \(-0.249210\pi\) | ||||
0.708860 | + | 0.705350i | \(0.249210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 60.1541 | 0.00981065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3638.91 | 0.588202 | 0.294101 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294101 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1015.19 | 0.161218 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1771.41 | −0.278854 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7965.23 | 1.23226 | 0.616132 | − | 0.787643i | \(-0.288699\pi\) | ||||
0.616132 | + | 0.787643i | \(0.288699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7699.35 | 1.18091 | 0.590454 | − | 0.807072i | \(-0.298949\pi\) | ||||
0.590454 | + | 0.807072i | \(0.298949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11674.7 | 1.76029 | 0.880144 | − | 0.474706i | \(-0.157446\pi\) | ||||
0.880144 | + | 0.474706i | \(0.157446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5841.50 | −0.873337 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2547.12 | 0.374463 | 0.187231 | − | 0.982316i | \(-0.440049\pi\) | ||||
0.187231 | + | 0.982316i | \(0.440049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5640.59 | 0.822363 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 610.973 | 0.0876158 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11020.0 | −1.56742 | −0.783708 | − | 0.621130i | \(-0.786674\pi\) | ||||
−0.783708 | + | 0.621130i | \(0.786674\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7942.81 | −1.11151 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8430.05 | 1.17022 | 0.585109 | − | 0.810955i | \(-0.301052\pi\) | ||||
0.585109 | + | 0.810955i | \(0.301052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1555.68 | −0.212524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1675.32 | 0.227059 | 0.113529 | − | 0.993535i | \(-0.463784\pi\) | ||||
0.113529 | + | 0.993535i | \(0.463784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12124.4 | 1.61757 | 0.808783 | − | 0.588108i | \(-0.200127\pi\) | ||||
0.808783 | + | 0.588108i | \(0.200127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1012.54 | 0.134035 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15159.1 | −1.97583 | −0.987916 | − | 0.154992i | \(-0.950465\pi\) | ||||
−0.987916 | + | 0.154992i | \(0.950465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2227.32 | 0.288083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2208.34 | 0.281301 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3884.64 | −0.491095 | −0.245547 | − | 0.969385i | \(-0.578968\pi\) | ||||
−0.245547 | + | 0.969385i | \(0.578968\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7056.99 | −0.878825 | −0.439413 | − | 0.898285i | \(-0.644813\pi\) | ||||
−0.439413 | + | 0.898285i | \(0.644813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5812.24 | 0.718432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3582.97 | 0.436366 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7034.26 | 0.850420 | 0.425210 | − | 0.905095i | \(-0.360200\pi\) | ||||
0.425210 | + | 0.905095i | \(0.360200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16169.7 | −1.92654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2142.91 | −0.253473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6153.56 | 0.717473 | 0.358737 | − | 0.933439i | \(-0.383208\pi\) | ||||
0.358737 | + | 0.933439i | \(0.383208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13024.0 | −1.50772 | −0.753862 | − | 0.657033i | \(-0.771811\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1507.93 | 0.172107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17179.9 | 1.94706 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11614.6 | 1.29805 | 0.649023 | − | 0.760769i | \(-0.275178\pi\) | ||||
0.649023 | + | 0.760769i | \(0.275178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1245.75 | 0.138260 | 0.0691301 | − | 0.997608i | \(-0.477978\pi\) | ||||
0.0691301 | + | 0.997608i | \(0.477978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4128.47 | −0.451926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7984.30 | 0.868041 | 0.434020 | − | 0.900903i | \(-0.357095\pi\) | ||||
0.434020 | + | 0.900903i | \(0.357095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13840.8 | 1.48442 | 0.742210 | − | 0.670167i | \(-0.233778\pi\) | ||||
0.742210 | + | 0.670167i | \(0.233778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7746.18 | 0.825178 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7756.38 | −0.815247 | −0.407624 | − | 0.913150i | \(-0.633642\pi\) | ||||
−0.407624 | + | 0.913150i | \(0.633642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4150.39 | −0.433336 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5797.07 | 0.597298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16107.6 | 1.64875 | 0.824377 | − | 0.566041i | \(-0.191526\pi\) | ||||
0.824377 | + | 0.566041i | \(0.191526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6272.71 | −0.633730 | −0.316865 | − | 0.948471i | \(-0.602630\pi\) | ||||
−0.316865 | + | 0.948471i | \(0.602630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18657.9 | 1.87280 | 0.936399 | − | 0.350937i | \(-0.114137\pi\) | ||||
0.936399 | + | 0.350937i | \(0.114137\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16289.5 | 1.61411 | 0.807054 | − | 0.590478i | \(-0.201061\pi\) | ||||
0.807054 | + | 0.590478i | \(0.201061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −298.244 | −0.0293638 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 396.394 | 0.0385333 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2795.04 | −0.269990 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11328.9 | −1.08065 | −0.540324 | − | 0.841457i | \(-0.681698\pi\) | ||||
−0.540324 | + | 0.841457i | \(0.681698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20513.5 | 1.94457 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2500.68 | 0.234124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14122.4 | 1.31406 | 0.657029 | − | 0.753866i | \(-0.271813\pi\) | ||||
0.657029 | + | 0.753866i | \(0.271813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5220.81 | 0.479861 | 0.239931 | − | 0.970790i | \(-0.422875\pi\) | ||||
0.239931 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2006.31 | 0.183286 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28962.1 | 2.61394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17934.3 | 1.60892 | 0.804459 | − | 0.594008i | \(-0.202455\pi\) | ||||
0.804459 | + | 0.594008i | \(0.202455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7305.37 | −0.647576 | −0.323788 | − | 0.946130i | \(-0.604956\pi\) | ||||
−0.323788 | + | 0.946130i | \(0.604956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2679.68 | 0.236127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6083.17 | −0.529728 | −0.264864 | − | 0.964286i | \(-0.585327\pi\) | ||||
−0.264864 | + | 0.964286i | \(0.585327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3029.20 | −0.262239 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 674.527 | 0.0577150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2026.13 | 0.172358 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10005.0 | −0.841316 | −0.420658 | − | 0.907219i | \(-0.638201\pi\) | ||||
−0.420658 | + | 0.907219i | \(0.638201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12931.9 | −1.08121 | −0.540607 | − | 0.841276i | \(-0.681805\pi\) | ||||
−0.540607 | + | 0.841276i | \(0.681805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7495.89 | −0.619594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10803.4 | −0.887927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23762.2 | −1.93106 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4043.15 | 0.326730 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2218.22 | −0.177264 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13088.9 | 1.04017 | 0.520087 | − | 0.854113i | \(-0.325900\pi\) | ||||
0.520087 | + | 0.854113i | \(0.325900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5369.79 | 0.422049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4522.72 | −0.353524 | −0.176762 | − | 0.984254i | \(-0.556562\pi\) | ||||
−0.176762 | + | 0.984254i | \(0.556562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3718.82 | −0.287526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10949.0 | −0.841948 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5477.36 | 0.416667 | 0.208333 | − | 0.978058i | \(-0.433196\pi\) | ||||
0.208333 | + | 0.978058i | \(0.433196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2269.47 | 0.171715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17369.7 | −1.30026 | −0.650129 | − | 0.759824i | \(-0.725285\pi\) | ||||
−0.650129 | + | 0.759824i | \(0.725285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2616.88 | −0.194855 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7997.66 | 0.589243 | 0.294622 | − | 0.955614i | \(-0.404806\pi\) | ||||
0.294622 | + | 0.955614i | \(0.404806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14623.1 | 1.07173 | 0.535864 | − | 0.844305i | \(-0.319986\pi\) | ||||
0.535864 | + | 0.844305i | \(0.319986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 923.170 | 0.0669545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3818.29 | −0.275490 | −0.137745 | − | 0.990468i | \(-0.543985\pi\) | ||||
−0.137745 | + | 0.990468i | \(0.543985\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10624.5 | 0.758657 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2617.35 | 0.185934 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19568.8 | 1.37597 | 0.687983 | − | 0.725726i | \(-0.258496\pi\) | ||||
0.687983 | + | 0.725726i | \(0.258496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13894.1 | 0.971977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5170.99 | −0.358090 | −0.179045 | − | 0.983841i | \(-0.557301\pi\) | ||||
−0.179045 | + | 0.983841i | \(0.557301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7476.32 | −0.515125 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10252.3 | −0.699327 | −0.349663 | − | 0.936875i | \(-0.613704\pi\) | ||||
−0.349663 | + | 0.936875i | \(0.613704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21251.0 | −1.44234 | −0.721168 | − | 0.692760i | \(-0.756395\pi\) | ||||
−0.721168 | + | 0.692760i | \(0.756395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6321.34 | 0.424792 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18653.8 | −1.24734 | −0.623669 | − | 0.781689i | \(-0.714359\pi\) | ||||
−0.623669 | + | 0.781689i | \(0.714359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11600.2 | 0.768076 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6156.56 | 0.405646 | 0.202823 | − | 0.979215i | \(-0.434988\pi\) | ||||
0.202823 | + | 0.979215i | \(0.434988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16106.4 | 1.05092 | 0.525461 | − | 0.850818i | \(-0.323893\pi\) | ||||
0.525461 | + | 0.850818i | \(0.323893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27462.5 | −1.78322 | −0.891608 | − | 0.452807i | \(-0.850423\pi\) | ||||
−0.891608 | + | 0.452807i | \(0.850423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38405.6 | −2.46980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26455.7 | −1.67704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9282.80 | −0.585646 | −0.292823 | − | 0.956167i | \(-0.594595\pi\) | ||||
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 573.648 | 0.0358496 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12699.9 | −0.789937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22076.4 | 1.36032 | 0.680160 | − | 0.733064i | \(-0.261910\pi\) | ||||
0.680160 | + | 0.733064i | \(0.261910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25416.1 | 1.55881 | 0.779403 | − | 0.626523i | \(-0.215522\pi\) | ||||
0.779403 | + | 0.626523i | \(0.215522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15054.7 | −0.914777 | −0.457389 | − | 0.889267i | \(-0.651215\pi\) | ||||
−0.457389 | + | 0.889267i | \(0.651215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5328.32 | 0.322273 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14629.6 | 0.876726 | 0.438363 | − | 0.898798i | \(-0.355558\pi\) | ||||
0.438363 | + | 0.898798i | \(0.355558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2495.37 | 0.148858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5302.96 | −0.313466 | −0.156733 | − | 0.987641i | \(-0.550096\pi\) | ||||
−0.156733 | + | 0.987641i | \(0.550096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7326.18 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13857.8 | 0.808094 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1228.28 | 0.0713034 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5661.22 | −0.325706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27965.1 | −1.60174 | −0.800872 | − | 0.598836i | \(-0.795630\pi\) | ||||
−0.800872 | + | 0.598836i | \(0.795630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17423.1 | −0.989103 | −0.494551 | − | 0.869148i | \(-0.664668\pi\) | ||||
−0.494551 | + | 0.869148i | \(0.664668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12398.4 | −0.700744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18318.0 | 1.02624 | 0.513118 | − | 0.858318i | \(-0.328490\pi\) | ||||
0.513118 | + | 0.858318i | \(0.328490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9436.91 | 0.526374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14985.1 | 0.828574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27603.8 | 1.51968 | 0.759838 | − | 0.650112i | \(-0.225278\pi\) | ||||
0.759838 | + | 0.650112i | \(0.225278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8924.50 | 0.487087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30645.5 | 1.66540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8448.22 | 0.455185 | 0.227593 | − | 0.973756i | \(-0.426915\pi\) | ||||
0.227593 | + | 0.973756i | \(0.426915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49037.2 | 2.63083 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13285.9 | −0.706741 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14440.0 | 0.764889 | 0.382444 | − | 0.923979i | \(-0.375082\pi\) | ||||
0.382444 | + | 0.923979i | \(0.375082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4589.05 | −0.241040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1910.28 | −0.0999166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24213.5 | −1.25593 | −0.627964 | − | 0.778242i | \(-0.716112\pi\) | ||||
−0.627964 | + | 0.778242i | \(0.716112\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3344.31 | −0.172744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 831.567 | 0.0425981 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10688.4 | −0.545271 | −0.272636 | − | 0.962117i | \(-0.587895\pi\) | ||||
−0.272636 | + | 0.962117i | \(0.587895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2926.88 | −0.148091 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18715.7 | −0.943085 | −0.471542 | − | 0.881843i | \(-0.656303\pi\) | ||||
−0.471542 | + | 0.881843i | \(0.656303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 98.2788 | 0.00491200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13155.2 | 0.654832 | 0.327416 | − | 0.944880i | \(-0.393822\pi\) | ||||
0.327416 | + | 0.944880i | \(0.393822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20680.3 | −1.02111 | −0.510557 | − | 0.859844i | \(-0.670561\pi\) | ||||
−0.510557 | + | 0.859844i | \(0.670561\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4981.60 | 0.244982 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20045.9 | −0.977921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −76.2198 | −0.00370346 | −0.00185173 | − | 0.999998i | \(-0.500589\pi\) | ||||
−0.00185173 | + | 0.999998i | \(0.500589\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17435.7 | 0.840463 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15781.3 | 0.757701 | 0.378851 | − | 0.925458i | \(-0.376319\pi\) | ||||
0.378851 | + | 0.925458i | \(0.376319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32298.0 | 1.53851 | 0.769253 | − | 0.638944i | \(-0.220629\pi\) | ||||
0.769253 | + | 0.638944i | \(0.220629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26623.4 | −1.26321 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30506.2 | 1.43613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6530.51 | −0.306237 | −0.153119 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153119 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8952.60 | −0.416562 | −0.208281 | − | 0.978069i | \(-0.566787\pi\) | ||||
−0.208281 | + | 0.978069i | \(0.566787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3106.86 | −0.144002 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56803.2 | −2.61256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9543.75 | −0.437263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8929.93 | 0.406016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15275.5 | −0.691886 | −0.345943 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345943 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12974.5 | 0.583211 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32412.1 | −1.45143 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42475.4 | 1.88777 | 0.943887 | − | 0.330267i | \(-0.107139\pi\) | ||||
0.943887 | + | 0.330267i | \(0.107139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14960.5 | −0.662408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 998.197 | 0.0438675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4577.07 | −0.200398 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39893.7 | −1.73373 | −0.866864 | − | 0.498544i | \(-0.833868\pi\) | ||||
−0.866864 | + | 0.498544i | \(0.833868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8645.69 | −0.374342 | −0.187171 | − | 0.982327i | \(-0.559932\pi\) | ||||
−0.187171 | + | 0.982327i | \(0.559932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1981.18 | 0.0851508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5425.14 | 0.232315 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42123.4 | −1.79064 | −0.895320 | − | 0.445424i | \(-0.853053\pi\) | ||||
−0.895320 | + | 0.445424i | \(0.853053\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17950.5 | 0.760287 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19430.2 | 0.816994 | 0.408497 | − | 0.912760i | \(-0.366053\pi\) | ||||
0.408497 | + | 0.912760i | \(0.366053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23552.0 | −0.986724 | −0.493362 | − | 0.869824i | \(-0.664232\pi\) | ||||
−0.493362 | + | 0.869824i | \(0.664232\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16378.8 | 0.681261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8747.42 | −0.362535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15526.2 | 0.638883 | 0.319442 | − | 0.947606i | \(-0.396505\pi\) | ||||
0.319442 | + | 0.947606i | \(0.396505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23282.6 | −0.954635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.0977 | 0.00195812 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31341.2 | −1.27142 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16196.4 | −0.652417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6582.11 | −0.264205 | −0.132103 | − | 0.991236i | \(-0.542173\pi\) | ||||
−0.132103 | + | 0.991236i | \(0.542173\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41261.8 | 1.64466 | 0.822332 | − | 0.569009i | \(-0.192673\pi\) | ||||
0.822332 | + | 0.569009i | \(0.192673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2460.09 | −0.0977149 | −0.0488575 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488575 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38478.8 | 1.51777 | 0.758884 | − | 0.651226i | \(-0.225745\pi\) | ||||
0.758884 | + | 0.651226i | \(0.225745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14994.8 | 0.589408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3607.95 | 0.140842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 562.675 | 0.0218892 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3098.75 | −0.119722 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28139.7 | 1.08348 | 0.541739 | − | 0.840547i | \(-0.317766\pi\) | ||||
0.541739 | + | 0.840547i | \(0.317766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14885.8 | 0.569257 | 0.284629 | − | 0.958638i | \(-0.408130\pi\) | ||||
0.284629 | + | 0.958638i | \(0.408130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22144.8 | −0.843979 | −0.421989 | − | 0.906601i | \(-0.638668\pi\) | ||||
−0.421989 | + | 0.906601i | \(0.638668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24626.1 | 0.932202 | 0.466101 | − | 0.884732i | \(-0.345658\pi\) | ||||
0.466101 | + | 0.884732i | \(0.345658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2844.14 | −0.107300 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27730.1 | 1.03914 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3413.75 | −0.127496 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4133.69 | −0.153355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19325.9 | −0.714583 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −296.972 | −0.0109079 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18461.8 | −0.675871 | −0.337935 | − | 0.941169i | \(-0.609729\pi\) | ||||
−0.337935 | + | 0.941169i | \(0.609729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44797.5 | −1.62921 | −0.814603 | − | 0.580018i | \(-0.803045\pi\) | ||||
−0.814603 | + | 0.580018i | \(0.803045\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3501.05 | −0.126909 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12372.0 | −0.445540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46730.6 | −1.67737 | −0.838684 | − | 0.544618i | \(-0.816675\pi\) | ||||
−0.838684 | + | 0.544618i | \(0.816675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54640.7 | −1.94856 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10965.2 | −0.389767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8092.99 | 0.285815 | 0.142908 | − | 0.989736i | \(-0.454355\pi\) | ||||
0.142908 | + | 0.989736i | \(0.454355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30359.0 | −1.06872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2463.64 | 0.0861706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40337.2 | −1.40636 | −0.703180 | − | 0.711012i | \(-0.748237\pi\) | ||||
−0.703180 | + | 0.711012i | \(0.748237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17800.7 | −0.616668 | −0.308334 | − | 0.951278i | \(-0.599771\pi\) | ||||
−0.308334 | + | 0.951278i | \(0.599771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18761.4 | 0.647886 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3077.80 | 0.105612 | 0.0528062 | − | 0.998605i | \(-0.483183\pi\) | ||||
0.0528062 | + | 0.998605i | \(0.483183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5714.97 | 0.195486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15297.9 | 0.519986 | 0.259993 | − | 0.965611i | \(-0.416280\pi\) | ||||
0.259993 | + | 0.965611i | \(0.416280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18090.6 | −0.612983 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46788.2 | −1.57546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14346.9 | −0.481585 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7681.85 | −0.256257 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22338.3 | −0.742865 | −0.371433 | − | 0.928460i | \(-0.621133\pi\) | ||||
−0.371433 | + | 0.928460i | \(0.621133\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14686.2 | −0.485378 | −0.242689 | − | 0.970104i | \(-0.578030\pi\) | ||||
−0.242689 | + | 0.970104i | \(0.578030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44247.6 | −1.45788 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31945.7 | 1.04609 | 0.523047 | − | 0.852304i | \(-0.324795\pi\) | ||||
0.523047 | + | 0.852304i | \(0.324795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12655.6 | 0.413151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18534.7 | 0.601389 | 0.300694 | − | 0.953721i | \(-0.402782\pi\) | ||||
0.300694 | + | 0.953721i | \(0.402782\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −682.354 | −0.0220727 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1791.86 | −0.0576116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31869.1 | −1.02155 | −0.510775 | − | 0.859714i | \(-0.670641\pi\) | ||||
−0.510775 | + | 0.859714i | \(0.670641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 616.275 | 0.0196354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7832.72 | 0.248811 | 0.124406 | − | 0.992231i | \(-0.460298\pi\) | ||||
0.124406 | + | 0.992231i | \(0.460298\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.4.a.f.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.l.1.3 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bh.1.1 | 3 | |||
12.11 | even | 2 | 2160.4.a.bp.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.l.1.3 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bh.1.1 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bp.1.1 | 3 | 12.11 | even | 2 |